But the M-W is definitely wrong in this case, true? How does one determine
which
is the right source? Do you just search until you find a source that supports
your position?

Most people will, indeed, search just long enough to find one source or another
that supports their position and hang on for dear life against all evidence or
opposition.

Those more interested in seeking truth will
consider multiple perspectives, drawing comparisons between what others have
observed and personal, contemporary observations. The mentally adept often seek
out contradictory opinions and examine them carefully for any elements of
greater or lesser truth they may contain.
The self righteous and intellectually insecure fearfully eschew dissenting
ideas.

Much depends on motivation. Some want to appear "right" (or righteous) at any
cost. Others want to get closer to the unvarnished truth, even if it ultimately
requires changing a long-held prinicple or considering a new idea.

No single source is an authority on everything. Even dictionaries are compiled
and edited by committees that often make arbitrary or underinformed decisions.
That is one of the reasons for consulting multiple sources, as the odds of
several editorial boards making identical arbitrary or underinformed decisions
are rather low.